Turn on a multi-functional pressure cooker (such as Instant Pot) and select Saute function. Melt butter in the pot. Add shallot and saute for 1 minute. Add garlic and ginger to the pot and saute for 1 minute more.
Pour in sherry and scrape the bottom of the pot to loosen any browned bits. Allow sherry to cook for 3 minutes, then push Cancel. Stir in the chicken broth, soy sauce, and pepper. Add shrimp to the pot.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 1 minute. Allow 5 to 10 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Stir in 2 tablespoons green onions and sesame oil. Garnish with sesame seeds and remaining green onions.